Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
2. Suppose that g: I→ R is differentiable at x = xo. Does the following limit g(xo +6h) - g(xo - 6h) 12h exist? (Either prove your answer or give a counterexample). lim h→0 Is the converse true? That is suppose the limit lim h→0 g(xo +6h) - g(xo - 6h) 12h L exists, is g differentiable at x = = xo? (Either prove your answer or give a coun- terexample).

2. Suppose that g: I→ R is differentiable at x = xo. Does the following limit g(xo +6h) - g(xo - 6h) 12h exist? (Either prove your answer or give a counterexample). lim h→0 Is the converse true? That is suppose the limit lim h→0 g(xo +6h) - g(xo - 6h) 12h L exists, is g differentiable at x = = xo? (Either prove your answer or give a coun- terexample).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
100%

Need help with the converse bit, use the example attached for the method for solving this question.

Conversely, suppose (1) holds and r=0(x-xo) Substituling x = xo in (1) we get B=f(x) lim (fix) +(20) - m) = . 0 x-xo (im Ff(x) x27x0 (x-xo) It follows that if then = lim √(22) > хэль (х-хо) lim f(x)-floco). 2-720 (2-20) = M m 20, => M= m= f'(an);
Transcribed Image Text:Conversely, suppose (1) holds and r=0(x-xo) Substituling x = xo in (1) we get B=f(x) lim (fix) +(20) - m) = . 0 x-xo (im Ff(x) x27x0 (x-xo) It follows that if then = lim √(22) > хэль (х-хо) lim f(x)-floco). 2-720 (2-20) = M m 20, => M= m= f'(an);
2. Suppose that g: I → R is differentiable at x = xo. Does the following limit - g(xo +6h) — g(xo – 6h) 12h exist? (Either prove your answer or give a counterexample). lim h→0 Is the converse true? That is suppose the limit lim h→0 g(xo +6h) - g(xo - 6h) 12h = exists, is 9 differentiable at x = xo? (Either prove your answer or give a coun- terexample).
Transcribed Image Text:2. Suppose that g: I → R is differentiable at x = xo. Does the following limit - g(xo +6h) — g(xo – 6h) 12h exist? (Either prove your answer or give a counterexample). lim h→0 Is the converse true? That is suppose the limit lim h→0 g(xo +6h) - g(xo - 6h) 12h = exists, is 9 differentiable at x = xo? (Either prove your answer or give a coun- terexample).
Expert Solution
steps

Step by step

Solved in 3 steps with 12 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS